Section Headings
The previous chapter showed that Attention Logic and LA Logic share a similar logical structure, i.e. are isomorphic. The current chapter shows that Attention Logic and Matter Logic are incompatible, i.e. not isomorphic. Because of these irreconcilable differences, the type of mathematical systems that apply to Matter can never effectively model Attention.
To achieve this end, we show that Matter belongs to an atomistic system, while Attention belongs to a holistic system. To better understand the underlying logical structure of holistic systems, we examine the underlying logic of music, which belongs to another holistic system. To better understand the underlying logical structure of atomistic systems, we examine the underlying logic of pictures, which belong to another atomistic system.
The underlying logics of the two types of systems are qualitatively different (not isomorphic). Atomistic systems have a bottom-up organization, where the parts determine the nature of the whole. Holistic systems have a top-down organization, where the whole determines the nature of the parts. Identifying the nature of permanent content is of utmost importance for an understanding of atomistic systems. Identifying the nature of dynamic contextual relationships is of utmost importance for an understanding of holistic systems.
Because they belong to qualitatively different logical systems, Attention and Matter require languages that are also qualitatively different. For this reason, the mathematical languages that so effectively model the behavior of Matter will never be able to model the behavior of Attention.
Attention and Matter are joined in every living system from single cells to multi-cellular humans. Traditional Dynamics certainly provides an excellent map for material behavior. Further, evidence indicates that Data Stream Dynamics provides a rough map the rhythms of Attention. In the terminology we have developed, Material Dynamics has many logical congruencies with Matter, while DS Dynamics is logically congruent with Attention. Both Math-Fact Matrices (Matter and Attention) are isomorphic systems.
Life = Attention x Matter
DS Dynamics Logic ≈ Attention Logic
Traditional Dynamics Logic ≈ Material Logic
Why has Material Dynamics been unable to model Attention? Why haven’t scientists, despite countless attempts, been able to match the logic of material systems with the logic of Attention?
Could it be that the logical structure associated with the two systems is incompatible, i.e. not isomorphic? Is it possible that Attention and Matter coexist and even interact in a common system (Life) yet possess inferential structures that are qualitatively different (not isomorphic)? Put another way, maybe Attention Logic does not equal Matter Logic.
Attention Logic ≠ Material Logic?
How could two logical structures be incompatible? Many hold the implicit belief that a singular logic governs a singular reality – a type of monism. This article develops the notion that Attention and Matter, although joined under the one roof of living systems, belong to two different logical systems – a type of dualism.
Despite being incompatible, each half of the logical dualism is incomplete without the other. In other words, neither half can completely describe their common system. The two systems represent two approaches to understanding. For instance, in botany there is both classification (content) and ecological relationships (context). Although sometimes incompatible, the dualisms complete each other.
If these were just two types of approaches, 2 cognitive tools, then they would not be called a duality. However as we shall see, living systems consist of both Attention, which belongs to contextual, holistic system, and Matter, which belongs to a content-based, atomistic system.
Our intention is to show that the systems associated with Attention and Matter form a logical dualism. They are both joined and even interact in living systems. Yet there are irreconcilable differences between the implicit logic of the two systems. Due to this inherent incompatibility, neither is a subsystem of the other. Further, the logic of one cannot be applied to the other, except in a superficial manner.
How are we to understand the logical dualism formed by Attention and Matter?
As mentioned the conceptual, not literary, metaphor is the basis of the abstract thought (deeper understanding) that informs our choices. We employ the implicit logic of something we understand – a known system – to understand the implicit logic of something we don’t understand – an unknown system. This inferential process is the essence of isomorphic logic. To better comprehend the Attention/Matter dualism, we will examine two other logical dualisms. Examining the logical structures of systems we understand will enable us to better grasp the nuances of the Attention/Matter dualism.
One of the dualisms is embodied in our senses – the sound/sight duality. Philosophers have identified the other – the holism/atomism dualism. As this second perspective addresses abstract systems rather than reality, we deem this to be a meta-dualism. Under this way of thinking, the two logical dualisms formed by Attention/Matter and sound/sight could be considered subsets of the holism/atomism dualism.
This discussion is not exhaustive. There can certainly be more than two types of system logic. However, the dualisms we have chosen have proven instructive regarding the Attention/Matter dualism. In fact, the three dualisms provide a feedback loop of understanding.
Due to its meta nature, let us start by examining the logical dualism composed of atomism/holism. What is holism and why is it different than atomism? Following is Brook Ziporyn’s definition of the word ‘atomism’ from his book1 that delves into the topic.
“‘Atomism’ is the view that the real nature of a thing is what it is in itself, removed from relations, and the best way to understand something is to analyze the nature of its constituent parts rather than how they are related or how it behaves as a whole in its relation with other things. If we know the nature of the parts, in this view, we know that nature of the compound they form. Holistic views, on the contrary, hold that the nature of the compound, or whole, must be understood in terms of its relation to other things and of the relation among whatever component it comprises.” P. 28
Summarizing the salient parts: an atomistic system is one in which the nature of the individual parts is independent of the whole. Understanding the nature of the component parts can be used to determine the nature of the whole. Because of the importance of the parts, identifying content is of utmost importance.
Ziporyn provides a contrasting definition of holism.
“Holism thus defines ‘parts’ and ‘wholes’ in such a way that the parts in a whole obtain their meaning from their contextualization in that whole and are altered, in all aspects of their being, by their relationship with the other parts. The context in which a part appears changes its meaning, significance, and character. The nature of each part is modified by the whole of which it is a part, which means also, inter alia, by all the other items, or parts, to which it bears a relationship.” P. 28
Summarizing: a holistic system is one in which the nature of the individual parts is dependent upon the whole for meaning. The contextual relationships between the parts is far more important the content.
The logic of atomistic and holistic systems is qualitatively different. In holism, context is of utmost importance. The contextual relationship between the whole and the parts determines meaning. This is the complete opposite of atomism. Content, rather than context and relationships, is of utmost importance to the atomist perspective.
Atomistic = Content-based
Holistic = Contextual-based relationships
Due to relative importance of the parts, atomistic systems have a bottom-up organization. Due to the relative importance of the whole, holistic systems have a top down organization. In the first, the parts shape the whole; in the second, the whole shapes the parts.
Atomistic = Bottom-Up = Parts shape Whole
Holistic = Top-Down = Whole shapes Parts
Reductionism is the method that is employed to investigate atomistic systems. Break a system into its component parts, e.g. atoms, in order to understand the whole, e.g. the molecule. The investigation centers upon finding the building blocks of the system. Investigating holistic systems entails an examination of the system’s gestalt, i.e. the parts in relationship to the whole, e.g. how changing the context changes the meaning.
How does this logical dualism apply to the Matter/Attention dualism? Exclusively material systems are atomistic. The spectacular successes of the material sciences are based upon examining smaller and smaller parts to determine their effect upon the whole. Rather than atomism, it seems to be more instructive to view a significant feature of living systems through the lens of holism. For instance, our survival as an organism is based upon a healthy relationship between our many subsystems (parts).
Material Systems = Atomistic Systems
Living Systems = Holistic Systems
We can dismantle a material system, such as a machine, and then reassemble it. In contrast, dismantling a living system results in dissolution – death. The process of breaking it into parts transforms the previously living system into an inanimate (dead) material system. The survival of the whole is dependent upon the parts.
Content is important for atomistic systems. Similarly, absolute content is crucial for determining the behavior of material systems. For example, an atom always behaves the same for eternity, always reacting identically under the same circumstances. Context is important for holistic systems. Similarly, contextual relationships are far more crucial for determining the behavior of living systems. Take the simple appetite. When hungry, we place a high value upon data streams associated with sustenance. When full, these same food data streams have lost their appeal.
It seems that living systems and holistic systems share a similar logic. In both cases, the whole shapes the parts in a top-down organization and contextual relationships are more important than content. Material systems and atomistic systems also share a similar logic. In both cases, the parts shape the whole in a bottom-up organization and content is more important the context.
Living Systems Logic ≈ Holistic Systems Logic
Material Systems Logic ≈ Atomistic Systems Logic
Note that the features of the two parts of the logical dualisms are quite different – content vs. context and top-down vs. bottom up organization. In other words, the logic of holistic systems is incompatible with the logic of atomistic systems and by extension Life’s logic is incompatible with Matter’s logic. There is no meta-logic that unites the systems to provide absolute truth.
Living Logic ≠ Atomistic Logic
Material Logic ≠ Holistic Logic
However despite these dissimilarities, both types of logical structures are necessary to understand the whole living system of which they are part. In other words, we can’t ask the question which perspective is true and which is false. The two alternate perspectives illuminate different parts of the unified system, i.e. the organism.
Living Logic x Material Logic = Living Organism
But enough abstractions, let us proceed to the concrete, something everyone has experienced first hand, the logic of our senses.
Systems can be categorized as atomistic or holistic. Generally speaking, material systems are atomistic, while living systems are holistic. The underlying logical structure of the two types of systems is qualitatively different, e.g. parts shape whole vs. whole shapes the parts. For this reason, we call these logical dualisms. We will now examine a logical dualism that is embodied in our senses: sight and sound.
Cognitive scientists have studied the logic of sight in great detail. Visual logic is incredibly influential, as it provides many of the conceptual metaphors that are blended together to create the abstractions of our everyday life. As an indication of its importance in our thinking, there are many visual words that are equated with understanding. The word ‘see’ is the most basic synonym in this regard. Insight is another. Nobody ever asks if you’ve had an in-sound. Of even greater technological significance, cognitive scientists have shown that the logic of traditional mathematics derives primarily from the logic of sight2.
Rather than delving into all the scientific complexities, which is beyond our scope, this discussion attempts to familiarize the reader with the logic of the senses by contrasting visual and auditory logic. There is definitely overlap as well as different aspects of sensory logic. To focus this discussion, we will primarily focus on the visual logic epitomized by a photograph, and the auditory logic epitomized by music.
Let us draw some immediate contrasts. The photograph is a static system of sight consisting of objects and background. It represents a single moment in time that can be experienced instantly and all at once.
In contrast, music is a dynamic system of sound consisting of notes. When we listen to music, we experience a range of feelings over time. These differences generate contrasting systems of logic.
Sight specializes in content – identifying objects. Indeed our visual cortex highlights contours in order to heighten the contrast between objects. Objectification is incredibly important for survival as it allows us to differentiate between a predator, prey and environment, e.g. tiger, zebra or moving grass.
We are using the snap shot/photograph to epitomize this type of visual logic. It characterizes a single moment in time. All the objects in the picture are generally well defined and permanent. The photo either contains an image of Uncle Gene or it doesn’t.
We can remove an object from a picture and place it elsewhere. Yet it remains the same object. This is the essence of the creative photo-shopping of pictures, e.g. placing a person in a group and location that is unknown to the individual.
Generally, there is no ambiguity in a photograph. The object is either a cat or it isn’t. There is no in-between, no middle ground of uncertainty.
According to cognitive linguists, the either-or logic of sight leads to logic of sets. An entity is either in the box or it isn’t. There is no middle. It is entirely possible to answer the question: Is the content inside or outside the set? Scientists successfully employ the set-based logic of sight to characterize the behavior of exclusively material systems.
Visual Logic -> Set Logic
Sound specializes in context. While we also identify objects with sound, the identification requires aural context. A snapshot (a moment) of sound is virtually meaningless. We must experience many auditory moments (sound over time) in order to understand the signal. For instance, we require many sounds to identify a birdcall or the crackling of leaves.
We are using music to epitomize auditory logic. In this case, dynamic context, rather than static content, is of utmost importance. The meaning of a single note is determined by its exact location in a piece of music. It has no meaning outside of this context.
The content of the notes is secondary to the relationships between notes, i.e. their context. The relationships between notes include the key and motifs. A composer introduces a particular theme. Then he might bring it back in a different key, or even invert the theme, perhaps in a different voice. The listener must remember and connect all of these twists and turns, even if subliminally, to truly appreciate the music. After some tortuous variations, the listener is rewarded – feeling comfortable like returning home to the familiar – when the piece returns to the opening theme.
The feeling the piece evokes is not permanent, but instead ever-changing. If permanent, the piece is relatively boring. For instance, the better composers create auditory expectations, e.g. perhaps modulating from major key happiness into minor key sadness within a measure or less. Expectations only exist from context and require a process to realize or violate them.
The visual logic of a photo is associated with the logic of static content, a state of permanence. In contrast, the auditory logic of music is associated with the logical structure associated with dynamic context. Does the content/context dichotomy sound familiar?
Visual Picture Logic ≈ ƒ (Static Content)
Auditory Music Logic ≈ ƒ (Relational Context)
Let us connect the dots. It appears that our three logical dualisms are isomorphic systems, albeit in a particular way. One half of each of the three dualisms is isomorphic with the rest and logically consistent internally. Yet the two halves of these logical dualisms are not isomorphic in the sense that there are logical inconsistencies between them. These similarities indicate that the internal logical structures of our three dualisms, i.e. Holism/Atomism, Attention/Matter, and Sound/Sight, are isomorphic.
Holism/Atomism Logic ≈ Attention/Matter Logic ≈ Sound/Sight Logic
Why call these logical dualisms? You might raise your eyebrows or roll your eyes at the specter of chaos, i.e. irresolvable logical conflicts. You might even wonder about the necessity of joining the two types of logical systems as a duality.
Strangely enough, we seem to require both perspectives, i.e. atomistic and holistic, in order to understand Life in her entirety. Her inanimate, exclusively material, content demands an atomistic approach, while her living side, i.e. the processes that strive for homeostasis to ensure the survival of the organism, demands a holistic approach. Either approach by itself, while consistent, is incomplete.
Life = Atomism x Holism
Stranger still, Evolution appears to have chosen two major distinct sensory apparatus, i.e. sight and sound, to encompass both perspectives. One objectifies reality by providing knowledge regarding objects, while the other provides knowledge regarding process. Why did natural evolutionary forces choose to embody the two types of logic, atomistic and holistic? Together they must provide a powerful language for understanding reality. Understanding certainly facilitates survival.
This makes sense as we exist as a living process within an inert object. Or put another way, we are a process that has been objectified as an organism. As a dynamic process that has been embodied, we attempt to facilitate the survival of the object we are encased in – maintaining it as a unified entity. Heaven has infused Earth with Life. Loving her temporary home, Life attempts to nourish, maintain and fulfill her potentials, whatever they may be.
Despite this affinity/this unity, object (Matter) and process (Life) obey distinctly different rules. As an atomistic system, Matter obeys the either-or set-based logic of sight. As a holistic system, Life obeys the both-and logic of music. In other words, the logical structures of the Object/Process Duality are not isomorphic.
Object (Matter) Logic ≠ Process (Life) Logic
Music is the language of the dynamic, transitory context-based feelings that dominate and motivate our living existence. Photos epitomize the language of the static permanent, content–based objects that we must negotiate in order to survive. Both of the logical processes are embodied in our sense of sound and sight. Both languages are required to understand Life’s dual nature. Understanding results in power.
Let’s check out the specific details of the isomorphic nature of the logical dualisms. Atomistic systems have a bottom-up organization, where the parts shape the nature of the whole. Content is of more importance than relationship. Set-based either-or logic applies to atomistic systems, because identifying elements puts them in a box. In this case, a reductionist approach is successful.
Material systems have a bottom-up organization, where atoms shape the nature of molecules, which in turn shape the nature of objects. Determining the absolute content of the tiniest particles enables one to understand the larger molecular structures. The set-based logic of the reductionist approach is applicable.
Photos also have a bottom-up organization, where objects shape the nature of the picture. Determining the contents enables the viewer to understand the picture. The Lehman family is in front of Angkor Wat in Cambodia. It must be a vacation picture.
Recall the congruities between the other halves of our logical dualisms. Holistic systems have a top-down organization, where the whole shapes the meaning of the parts. Dynamic relational context, not content, determines meaning.
Living Systems also have a top-down organization, where the organism shapes the meaning of the biological systems and cells it requires for survival. Dynamic contextual relationships between the systems and their cells, not content, determines meaning.
Music also has a top-down organization. The composition shapes the meaning of the notes it consists of. Dynamic contextual relationships between the individual notes and the whole, not content, determines meaning.
These relationships are shown in the following table.
| Atomistic | Matter | Pictures | Holistic | Attention | Music | |
|---|---|---|---|---|---|---|
| Parts shape Whole | 1 |
1 |
1 |
0 |
0 |
0 |
| Content-based | 1 |
1 |
1 |
0 |
0 |
0 |
| Bottom-Up | 1 |
1 |
1 |
0 |
0 |
0 |
| Either-Or | 1 |
1 |
1 |
0 |
0 |
0 |
| Whole shapes Parts | 0 |
0 |
0 |
1 |
1 |
1 |
| Context-based | 0 |
0 |
0 |
1 |
1 |
1 |
| Top-Down | 0 |
0 |
0 |
1 |
1 |
1 |
| Both-And | 0 |
0 |
0 |
1 |
1 |
1 |
Summarizing: atomistic, pictorial and material systems are content-driven and have a bottom-up organization. Further either-or set-based logic applies to these systems in that the content is either in the box or not. There is no other alternative. The middle is excluded.
In contrast, holistic, musical and living systems are driven by contextual relationships and have a top-down organization. Further reflexive logic applies to musical and living systems in that reflection upon what has gone before and anticipation of what is coming next determines meaning. Set-based logic does not apply because content is secondary to relational context. Both-and applies rather than either-or. The middle is not excluded.
We can draw two conclusions: 1) One half of each dualism is logically isomorphic with the others, i.e. a similar logical structure. 2) The two halves of these dualisms are not isomorphic, i.e. incompatible. In other words, the two halves of the dualism are qualitatively different in terms of implicit logical structure.
These relationships are summarized below in equation form:
Attention Logic ≈ Holistic Logic ≈ Music Logic
Matter Logic ≈ Atomistic Logic ≈ Picture Logic
Matter/Atomistic/Picture Logic ≠ Attention/Holistic/Music Logic
These isomorphic relationships, i.e. the equivalencies and incompatibilities in the system logic, indicate that the logics of Attention and Matter are also innately incompatible. Due to these irreconcilable differences, models that are aligned with one half of the dualism will never be able to model the other half. The logical structures of the two halves have inherent qualitative differences that prevent any kind of reconciliation. In other words, the traditional Mathematics that models Matter so perfectly will never be able to model Attention.
1 Brook Ziporyn, Evil and/or/as the Good: Omnicentrism, Intersubjectivity, and Value Paradox
2 Lakoff and Nunez, Where Mathematics Comes From, 2000, Basic Books